Sketch the graph of the curve y = (x – p)(x – p – 1)(x – p – 2) Shade the area of the region bounded by the curve, y = (x – p)(x –p – 1)(x – p – 2), the X – axis,x = 0 and x = p +3 Hence, find the area of the region using integration.

Q: Find the value(s) of c such that the area of the region bounded by the parabolae y=x2-c2 and y=c2-x2…

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Q: The value of the triple integral 2x² dV E where E is the region inside both x² + y? + z2 : z = -V3x2…

A: Here we will use cylindrical co ordinate to find triple integral  in cylindrical co ordinate  x = r…

Q: Rotate the region bounded by x = y² – 6y + 10 and x = 5 about the y-axis

A: Solution :-

Q: (b) Verify Green's theorem for |(x² – 2x y)d x+(x² y+3)d y, around the boundary e of the region y…

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Q: (a) Consider the region bounded by the graphs of y=c(2x-4), x-1, x-3. and y 0 where c is just a…

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Q: The double integral 2xy³dA over the rectangular region R {(x, y) E R“, 0 < xS 4 and – 1 S y< 0} is…

A: The double integral ∬Rfx, ydA can be written as ∬Rfx, ydxdy. We have given the rectangular region as…

Q: Consider 6x (1+x²)² 2(x+y) (1+x²)² + 2y ý = Using the function V(x, y) = 12 + y² show that the…

A: What is Lyapunov Stability Theorem: Lyapunov stability theorem says that if a function is positive…

Q: D. Use double integration to find the area of the region R enclosed by the parabola y = 4-x² and the…

A: Let's find area by using double integration.

Q: Evaluate the triple integral ∫∫∫T (x^2) dV where T is the tetrahedron with vertices (0, 0, 0), (1,…

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Q: Evaluate the integral. 9. dx J2 (x² - 1 1)3/2 Additional Materials Type here to search

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Q: 2 Evaluate 2 dA where D is the region described by 0s ys 55 - x Integral is equal to : Enter an…

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Q: . 3. Compute E y 2 z 2 dV , where E is the region bounded by x  1
y 2
z 2 and x 

A: The given curves are

Q: Evaluate the triple integral∭E xy dV where E is the solid tetrahedon with vertices…

A: Given Data : Triple Integral ∬∫ExydV and E is the solid tetrahedron with vertices 0,0,0,…

Q: The surface area of the surface generated by revolving y= 1 – x² for 0<x<1 about the x – axis is s=…

A: The solution is as follows

Q: (c) By using the Green's theorem, evaluate $(2xy) dx + (4x²y*) dy if C is the boundary of a region…

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Q: 9. Use Green's Theorem to evaluate (e* +y²) dx +(e" +x²) dy where C is the boundary of the region…

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Q: 4. Find the volume of the solid generated when the region bounded X - 2 by f(x) = x = 1, and the…

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Q: Evaluate the triple integral // x dV, where T is the solid tetrahedron with vertices T (0,0, 0),…

A: Here we have to evaluate the triple integral , where T is the solid tetrahedron with vertices…

Q: 1. Evaluate the double integral r²y dA, where D is the region enclosed by the x-axis and the…

A: We can evaluate the double integral.

Q: Evaluate the double integral I3 = S (21 – 4 2*) dxdy S where S is the region in the 4th quadrant (y…

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Q: 149. sin x cos ydx + (xy + cos x sin y)dy, where C is the boundary of the region lying between the…

A: We have to find ∫c sin x cos y dx +(xy+cos x siny)dy , where C is the boundary of the region lying…

Q: 2- Find D xyz dV where D is the region with -1 ≤x≤1, x ≤ y ≤ 1, above z = x, and below z = y + 2.

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Q: Find the area of the region described in the following exercise a. The region bounded by y=4x+4,…

A: Since you have asked multiple questions in a single request, we would be answering only first…

Q: Evaluate the double integral 4.x dydr 9 + y2 I when A is the shaded region in enclosed by the graphs…

A: Evaluate the double integral.

Q: Calculate an integral ∬R √ (x2 + y2)dA, where R is the region within the upper semicircle of radius…

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Q: Let R be the region in the half plane x 2 0 bounded by the curves y = -5x +5 y = x - 1 x = 0 Compute…

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Q: Let A be the region bounded by y = 8x 3(1−x) and the x-axis between x= 0 and x= 1. Find the solid…

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Q: and the y-axis. 2. Evaluate , 5x³ cos(y³) dA, where D is the region bounded by y = 2, y =:

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: The solid S is obtained by rotating the region enclosed by y = f(x) 2 0, a = 5+ 5e6 1- e6 5+ 5e16 1-…

A: The given question is solved below.

Q: Define R as the region bounded by the graphs of f(x) = 6x - 5x² and the x-axis. Which of the…

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Q: Determine the double integral || e2x-3ydxdy If the region is given as x = -1; x= 2 y =-2; 4x+ 2y 4…

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Q: integrate ƒ over the given region. ƒ(s, t) = e^s ln t over the region in the first quad-rant of the…

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Q: Evaluate 7x dV where E is the region that lies inside the cylinder x2 + y² = 8 E and between the…

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Q: of the ne Joint constant on the region (x, y) : x > 0n yleql n-0.5 < x - y < 0, sho in the image…

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Q: 1 Find the centroid of the area bounded by x2- 4y + 8 = 0, the lines x = 0 and x = 4, and the…

A: Formulas are written within the solution.

Q: The double integral ſſ 2xy³dA over the rectangular region R = {(x, y) E R², 0<x<4 and– 1<y<0}is…

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Q: (a) Calculate the centroid (7, y) of the region under the graph y = cos x for 0 < x <T/2.

A: Hi, since you have asked multiple questions, we will solve the first question for you. If want any…

Q: Define R as the region bounded by the graphs of f(x) = 2√x and g(x) = over the interval [0, 1].…

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Q: 2. Find the surface area of the solid generated by rotating the region bounded by the graphs of f(x)…

A: In this question we have to find the surface are of the solid region generated by rotating the…

Q: The numerical value of л за 3dA (where D is the region bounded by lines y=0 and x = 1, D and the…

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Q: Evaluate the triple integral -3pi D x dV where E is the solid bounded by the paraboloid x = 6y² +…

A: Solution is given below:

Q: Consider the integral x³+1 x³(x²+1) -dx What is the correct partial fractio OA Bx + C

A: We have to choose the correct option from the given options according to the given information

Q: (1) Sketch the regions of integration. (a) 7/2 Jo r3m/2 (b) (1r, 0)r drdo 3n/4

A: Consider the equation

Q: 4x Estimate the error in the quadratic approximation of f(x,y) = e sin y at the origin over the…

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Q: Let I = L S x+1 хdydx. %3D -1J-V1-x By reversing the order of integration of I, we obtain: Two…

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Q: Consider the region bounded by the graphs of y = ln x, y = 0, and x = e. d. Find the centroid of the…

A: Given the region

Q: The volume of the solid generated by the curve y = e¬ª, between x = 3 and x = 7 about the |3| x –…

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Q: Given ||(3x*y)dA , where R is the region bounded by y=0 and y = v9-x ². Sketch R the region of…

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Q: b) Evaluate [[ (3-4x)dV where E is the region below :=4-xy and above the region in the xy -plane…

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